Simplify the Radical Expression square root of 64m^3n^3

$\sqrt{64 m^{3}} n^{3}$

Step 1

Rewrite $64 m^{3}$ as ${(8 m)}^{2} m$ .

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2} m^{3}} n^{3}$

Factor out $m^{2}$ .

$\sqrt{8^{2} (m^{2} m)} n^{3}$

Rewrite $8^{2} m^{2}$ as ${(8 m)}^{2}$ .

$\sqrt{{(8 m)}^{2} m} n^{3}$

Step 2

Pull terms out from under the radical.

$| 8 m | \sqrt{m} n^{3}$

Step 3

Remove non-negative terms from the absolute value.

$8 | m | \sqrt{m} n^{3}$